SCHOOLS: Mathematics at mercy of trendy educators

by Kevin Donnelly

News Weekly, November 5, 2005

High school mathematics has been dumbed down, according to leading Australian educationalist Dr Kevin Donnelly.

And you thought high school English was being dumbed down. The report Comparison of Year 12 Pre-Tertiary Mathematics Subjects in Australia 2004-05 raises significant questions about the rigour and comparability of mathematics courses across Australia.

After reading it, one can't help but ask: Are students in different states adequately prepared for tertiary study?

In relation to comparability, the report concludes that mathematics courses across Australia "vary enormously, with differences in philosophy, mathematical content and assessment so great that no two states' Year 12 mathematics subjects could be described as equivalent".

The fact that courses are so dissimilar not only leads to the problem, when students move interstate, of there being a mismatch between what is expected in first year and what has been taught in Year 12, but some courses fail to provide a satisfactory preparation for tertiary study.

Requirements lowered

In the report's press release, Garth Gaudry notes: "We can say that in terms of the syllabus content, WA, SA and Queensland do not require students to study a number of core sub-topics of mathematics that are needed for tertiary studies in engineering, science, actuarial studies and other quantitative areas."

In relation to academic rigour, even though the report does not rank the different curriculum documents in as detailed a way as the recent benchmarking report analysing the primary school mathematics curriculum, there is a clear indication that some Year 12 courses are stronger than others.

As Gaudry puts it: "At the top end, the NSW four-unit mathematics subject is more ambitious than any other Australian Year 12 mathematics subject and sets a benchmark for very able students.

"Victoria offers students the opportunity to undertake the equivalent of a first-year university course as part of the [Victorian Certificate of Education].

"Very able students in other states are clearly disadvantaged in terms of challenging material. While there are good features of the mathematics courses offered across Australia, the point remains that expectations vary so much that students in some states are disadvantaged."

Of course, debates about mathematics should not be restricted to the senior school level. As commonsense suggests, what happens at the primary and lower secondary level has a vital impact on student interest in, and ability to cope with, mathematics in later years.

At the primary school level, there are a number of concerns. As noted by Max Stephens in the recent federally-funded benchmarking report analysing mathematics curriculum, Australian documents "without exception fail to provide clear guidance for teachers about what to teach at each year level".

Not only are Australian primary teachers overwhelmed by vague and fluffy statements of learning but, as Stephens's analysis concludes, the syllabus documents in California, Singapore and Japan are far more detailed, unambiguous and academically rigorous.

Such are the concerns about primary school curriculum that Rhonda Farkota, a research fellow at the Australian Council for Educational Research, concludes:

"Blaming our students' lack of basic mathematical skills on the transition years has long enabled us to hide from the brutal reality that mathematics teaching in Australian primary schools is in a state of crisis and confusion."

As a result of Australia's adoption of outcomes-based education, classrooms adopted fads such as student-centred learning and inquiry learning.

In part, the problem is that many of the academics responsible for teaching trainee teachers refuse to accept the importance of more explicit and content-based approaches to learning.

To quote Farkota: "Almost every teacher-education program in Australian universities is based on a student-directed approach arguing that mathematical ideas must be personally constructed by the students themselves.

"With all due respect, this is nonsense: it's unrealistic to expect children, unaided, to learn theories and concepts that have taken mathematicians millennia to put together."

Ideologically driven

John Ridd, a past member of the Queensland Board of Senior Secondary Studies, also suggests that mathematics teaching suffers from the impact of trendy educators, substandard curriculum documents and boards of education driven more by ideology than commonsense.

Many students no longer learn their times tables by rote, mental arithmetic has largely disappeared as a result of calculators, and algorithms such as long division are no longer taught.

The result, according to Ridd, is that "maths standards up to the end of Year 10 are known to be highly variable and frequently weak".

Much of the recent education debate has focused on English. Hopefully, the report analysing Year 12 mathematics courses will shift the debate to the other, equally important side of the education equation.